A. MacFadyen & W. Zhang (NYU), Alexandria

(Magneto-) Hydrodynamics of GRB

Outflows

2D Afterglow JetRelativistic MHD Turbulence

arXiv:0902.2396

arXiv:0811.3638

A. MacFadyen Banff URJA 7/14/05

GRB photons are made far away from engine.

Can’t observe engine directly with light. (neutrinos, gravitational waves?)

Electromagnetic process or neutrino annihilation to tap power of central compact object.

Hyper-accreting black hole or high field neutron star (rotating)

Relativistic Blastwave

10^52 ergeta = E/m > 100R = 1 = 3x10^10cm

n = 1 cm^-3

Blandford & McKee (1976)

Г >> 1

Self similarity

Fireball Acceleration

pressure Г-1

Log RLog R

AM & Zhang, Kobayashi, Piran & Sari (1999)

Required Resolution ~ 1/Г2

Transition to Non-relativistic

-3

-3/2

E = 10^52 erg

n = 1 cm^-3

Log (Г-1)

Log R

Erice, J. Wheeler School Andrew MacFadyen (NYU)

Please see talks by: Bucciantini, McKinney & Nagataki

AMR Collapsar Jet + Ni-56 rich Wind Magnetic Tower

Deceleration

• Relativistic E ~ Г2ρ R3 Г ~ R-3/2

• Jet “spreading” Г ~ 1/θjet

• Newtonian E ~ v2ρ R3 v2 ~ Г-1 ~ R-3

Erice, J. Wheeler School Andrew MacFadyen (NYU)

Collapsar vs. Magnetar

Uzdensky & AM (2007,2008)

Erice, J. Wheeler School Andrew MacFadyen (NYU)Uzdensky & AM (2006,2007), Kommisarov et al (2007), Bucciantini et al (2007), Dessart et al (2007)

Magnetic Tower

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Relativistic GRB Jet (AMR)

Erice, J. Wheeler School Andrew MacFadyen (NYU)

Adaptive Mesh Refinement (AMR) - Emery Step Test

Shear Flow Resolution

400

3200

51200

Smooth & Spherical

Clumpy & Spherical

Erice, J. Wheeler School Andrew MacFadyen (NYU)

Vorticity Generation

A ≡ (ρ1-ρ2)/(ρ1+ρ2)

ρ1

ρ2

∇P

∇ρ

ηt = k[u]Aη

Ultra-relativistic Vorticity and Shock DynamicsGoodman & MacFadyen (2008)

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Clumpy Medium

Jet & Shear

Jet & Clumps

Flying Pancakes

Misaligned

Oblique

Colliding Clumps

Shear Patches

Kelvin-Helmholtz Instability

Kelvin Helmholtz Clouds

Beverly Shannon

Big Whirls Have Little Whirls

Joly et al (2008)

2D Relativistic HD KH

Twisting and Folding

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KH:1024^3 Rel. MHD

Mag. & Kin. Energy

Power Spectra

AG Jet Initial Conditions

• Blandford-McKee• Eiso = 1e52 erg

• no = 1cm-3

• Г = 23.1• Θjet = 0.2, 0.4

• Spherical

• Ro = 1.59e17 cm

• R/ΔR = 196608

• 4e10 zone equiv.R

θ

Г = 23.1

Text

2D GRB Blastwave

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2D Blastwave (energy)

Energy Spreading

Light Curves

Zhang & MacFadyen (2009)

Light Surface

Volume

A. MacFadyen JAS McGill 9/8/05

TM EOS

e=0.5((9θ2+4)0.5+3θ-2) θ≡P/ρ Ultrarelativistic Г=4/3 Newtonian Г=5/3 e= θ/(Г-1)

Conclusions

(Mild) RMHD Turbulence has Kolmogorov-like

spectrum GRB AG Jets take > 10 years to isotropize

Newton vs. Relativistic HydroConservation of mass momentum, energy

j momentum coupled to i through Lorentz Factor

Relativistic when W>1 AND/OR

A. MacFadyen IPAM UCLA 5/3/05

Method

• WENO 5th order (Jiang & Shu ,1996)

• SRHD characteristic stucture (Donat et al 1998)

• Runge-Kutta 3rd order (Shu & Osher 1988)

• Also PLM reconstruction w/ minmod (Kurganov & Tadmor, 2000)

• F-WENO, F-PLM, U-PPM, U-PLM

• AMR from PARAMESH/FLASH2.3

Erice, J. Wheeler School Andrew MacFadyen (NYU)

5th order accuracyMethod N L1 Error Convergence Rate

Alpha

CR acceleration (prelim)

Zrake et al (2009)

CR acceleration (prelim)

Zrake et al (2009)

A. MacFadyen NYU 1/27/06

Collapsar – Relativistic AMR (2005)

• rho ~ 10^9 g/cm^3

• T ~ 10^10 K

• M_dot ~ 0.1 M_sun/s

• t_acc ~ 20 s

• R_in ~ 2 R_g

AM, Zhang, Woosley (2005)

Alpha

Zhang & MacFadyen (2009)

Zhang & MacFadyen (2009)

Zhang & MacFadyen (2009)

Blast Evolution

Zhang & MacFadyen (2009)

Spectra

Zhang & MacFadyen (2009)

2D Blastwave (density)

Zhang & MacFadyen (2009)